Shoulder joint prostheses are known in the art. See, for example, U.S. Pat. Nos. 4,919,669 and 5,738,161, hereby incorporated by reference. A typical shoulder prosthesis comprises a body, which is for implantation into a prepared humerus, and a head, which is fixed to the body and provides a bearing surface. Modular shoulder prostheses are also known. See, for example, U.S. Pat. No. 5,314,479, hereby incorporated by reference. U.S. Pat. No. 5,314,479 discloses a modular prosthesis comprising a body, which is implanted into the humerus, and a head, which seats onto the body. The head and body can be selected independently of each other, and head/body combinations can be selected by a surgeon to provide a custom fit without carrying a large expensive inventory of prostheses. A typical modular shoulder prosthesis, such as that disclosed in U.S. Pat. No. 5,314,479, also has a collar located between the head and the body. The collar sits on the prepared proximal surface of the humerus and provides a suitable surface for supporting the head. The collar, however, occupies joint space, and as compared to an analogous prosthesis of a non-modular design, a modular prosthesis with a collar may require additional joint space. This additional joint space may cause “overstuffing” of the glenohumeral joint, resulting in a decrease in range of motion. Also known are modular designs which have a collar integral with the body and provide a “low profile” modular connection. See, for example, U.S. Pat. No. 5,489,309, hereby incorporated by reference. However, use of these prostheses still may result in overstuffing and a loss of useful articular surface.